The goal of this work was to devise tools to speed up the modeling of membrane contours, particularly in tomograms where the membranes are grainy or variably distinct. Membranes are detected by correlation of the image with a set of kernels, or filters, oriented in a full range of directions. Each kernel is shaped like an inverted parabola along its long axis and like a Laplacian perpendicular to this axis. To follow a membrane from a given point, the program takes a small step from that point in the current direction of the membrane, then searches locally for the location and orientation at which a kernel gives the highest correlation. This gives the position and direction for the next iteration. Although this algorithm has greater than 95% accuracy in taking each individual step, it cannot follow an entire bounded contour without guidance in part, because of the large number of steps involved. However, we have successfully used the algorithm to implement a function for following a membrane between two existing model points. In practice, the operator uses the mouse to deposit a target model point on the membrane at some distance from the last point, then presses a key. The line tracker inserts model points between the two endpoints. If this inserted segment does not follow the membrane, the operator sees this immediately, presses a key to undo the action, then either models through a troublesome spot by hand or moves the target point closer to the last model point and tries the line tracker again. We have found that a skilled operator can anticipate which areas cannot be tracked automatically and thus can learn how to get the most benefit from the tool. Once a contour has been modeled on one tomographic slice, a related tool allows one to copy the contour to the adjacent slice and adjust its position to fit the membrane on that slice. Here the kernels used at any particular location are curved to follow the shape of the contour at that position, unlike the straight kernels used for the membrane tracker, which do not work well on highly curved regions of membrane. In practice, the operator first examines the adjacent slice, then if the membrane does not change too much presses a key to initiate the contour copying function. Small errors can then be corrected by hand if necessary. The combination of line tracking and contour copying functions has increased the speed of modeling Golgi membranes in tomograms by 3-4 fold.

National Institute of Health (NIH)
National Center for Research Resources (NCRR)
Biotechnology Resource Grants (P41)
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